In The Godfather II, Vito decides to get rid of Don Fanucci and kills him during the carnival outside his apartment. How could it be so easy to kill Don Fanucci? Supposedly with the career he got, killing him must have been of benefit for lots of people and he must have had lots of enemies that tried to kill him by that time. So he must have gotten himself some bodyguards. Why was there no trouble to kill him?
The book actually provides a better explanation than the movie does.
Shortly after young Vito Corleone looses his job at Genco due to Fanucci's threats to his boss, Vito witnesses Fanucci being physically attacked by two neighborhood kids. Fanucci calls for help, but to no avail. This is the point where Vito realizes that Fanucci is not untouchable.
In the novel and in the chronological film version re-edited for TV (The Godfather Saga), Vito witnesses an attack on Fanucci by two youths of the neighborhood who are tired of Fanucci's oppression over the neighborhood. Although Fanucci screams for help, nobody comes to his rescue and the attack ends only when the youths have robbed him, cut his throat, and run away. Vito knows from his own experiences that a real Don would probably be escorted by bodyguards, and that anybody who dared attack him would be dealt with severely and publicly. Vito begins to suspect that Fanucci's power comes from the threat of force rather than force itself.
Don Fanucci was able to terrorize the neighborhood of Little Italy and extort from local business owners because of his association with mafia boss Maranzalla.
Maranzalla was the leader of a criminal ring specializing in extortion, gambling and armed robbery. It was also rumoured that he was padrone to Fanucci, a known extortionist who relied on his connection with Maranzalla to remain 'untouchable'.
Don Fanucci did not have bodyguards. He felt untouchable. His arrogance coupled with the fact that the neighborhood was better off with him dead is how he was so easy to kill.
Fanucci was also despised by the police, so there was no investigation into his death. Nobody (including Maranzalla) cared that Don Fanucci was killed. Maranzalla did not attempt to find out who killed him to avenge his death.
I agree that Vito realized that Fanucci is not untouchable. To me, the reason Vito meets with Fanucci at the coffee shop before killing him is to truly test his level power. Vito brings Fanucci only 25% of the amount of money that he has demanded from Vito, Clemenza, and Tessio. It is telling to the Vito that Fanuci accepts this money without any level of major protest or threat. If Fanucci could really hurt Vito or have him arrested, he would do so. No one with true power would accept less money than demanded. Vito realizes from this act that Fanucci does not have any true power. He is masquerading as powerful and by taking Fanucci out of the equation, he can remove a perceived threat and also solidify his own power in the eyes of others.